Professional Sports and Diminishing Marginal Utility

Frequent commenterMattsubmits a guest post about the different incentives motivating professional athletes and those at the college level.

We've all heard or espoused this idea at some point: College sports is better than professional sports because the athletes are playing for "the love of the game." There are plenty of ways one could respond to this argument, but I believe that the argument is false. First off, let me just acknowledge that I probably like professional sports for reasons unrelated to what's under discussion here. However, there's nothing people like us enjoy doing more than creating fancy rationales to make whatever we support that much more justifiable. With that in mind, I'd like to offer my thesis: professional sports are more enjoyable to watch because professional athletes are actually playing for the love of the game.

I base this on a concept, known to fans of economics everywhere as "diminishing marginal utility" (henceforth referred to as "DMU.") The concept is straightforward and intuitive: if you're hot and thirsty, cold water provides you with the maximum level of pleasure, but by the time you consume your 5th liter it's providing significantly less pleasure. This concept is obviously applicable to the way we experience pleasure in the world, and it's also behind many such basic economic concepts like supply and demand curves, which are themselves based on "indifference curves." Indifference curves rely very heavily on the concept of DMU. Diminishing Marginal Utility = Declining Rate of Pleasure gained from a good or experience.

As harmless as the example about water sounds, there is a more radical application of DMU, and it's about income. Applying the concept of DMU you'd conclude that one dollar to starving person adds greater utility than does the same dollar given to Donald Trump. I think you may able to see where I'm going with this. Since the prospect of a million dollar contract has greater utility to a poor NCAA player than it does an 8th year NBA superstar, the same rich superstar has less incentive to play basketball for money than does the poor NBA hopeful. Sure the starting point guard for UNC has probably gotten his share of kickbacks, but his mother's still living in the same dump of a house, and he wants to play in order to provide for her. Allen Iverson, however, has already bought everyone he even remotely likes their own house, and therefore, the idea of playing only for a few more strangers' houses can't be as appealing. It follows then that Iverson must have different incentives than the point guard for UNC, and those likely are rooted in what's called "the love of the game."

As good libertarians you're probably apt to ask, what's so bad about being motivated by money? I'll tell you: in sports it causes rational restraint. Since the NCAA player is so heavily motivated by the prospect of money he has strong incentives to avoid injury, as that may jeopardize his chances of ever making money in the NBA. As a result, he plays with "rational restraint." In other words, as an individual he has an incentive to make the game less enjoyable for us as spectators- he "goes to the hole" less often, he dives for less loose balls, he asks to be taken out when he is tired. Obviously every basketball player has an interest in avoiding injury to some extent (though you'd hardly know it from watching a player like Allen Iverson) but in college ball, the incentive is heavily reinforced by economic incentives.

"Wait," you say. What about the college players who have no shot of going to the NBA, what about the fact that 90% of the college players never make it, what about the NBA players working for the NBA's minimum wage? Well, it's worth noting that the sort of ego you'd likely have from playing sports so well would probably make it difficult to rationally assess your odds of making it to the NBA. I should also point out that there are other incentives the lesser college players have in the form of scholarships, free anonymous sex, and "boosting." Regarding the rgument about the NBA's minimum wage, I will grant that 12th man on the Bulls' roster is probably quite heavily motivated by the desire to make more money, but what are we really talking about when we talk about why we watch the NBA vs the NCAA? We're talking about the players and teams that people actually tend to watch. Is your enjoyment of the NBA contingent on the motives behind a player for the Bulls who'll play for 5 minutes in the game? Of course not. Your enjoyment is contingent on the motives behind players like Kobe Bryant or Steve Nash. The same logic applies in reverse to most college sports. Is there some Rudy on the University of Montana basketball team who's got no shot of making it but just plays with a lot of heart? Of course there is, but whom do we actually watch? We watch the Duke play UNC in the Sweet 16, and we watch their star players, all of whom are going to the NBA, barring catastrophe. These players are motivated by money: the money they'll get from avoiding injury and playing in the NBA.

There's one reasonable counterargument to this: to attain the sort of skills necessary to play serious basketball in the national spotlight, basketball has to become such a dominant part of your life that outside motivators cease to matter. That argument says the question of motives is to a large degree meaningless, and that most players play because they simply have no idea what else to do. They don't know anything else. This actually sounds like the "love of the game" to me, albeit somewhat of a codependent, psychotic love. Even granting this point however, my basic point about the NBA is still reinforced, as it's clearly likely that you'd find a greater percentage of such "pathologically-in-love" players in the NBA since that quality is expected to be commensurate with skill-level. No one seriously doubts that the players are "better" in the NBA, so you'd expect the "national spotlight" illustration to hold to an even greater degree.

I didn't watch the Final Four this year, but I'm avidly watching the NBA finals and very much enjoying it. Rather than watch a bunch of players rest on their laurels so they'll get drafted and make a great living, I choose to watch players who already have so much money that they don't even have to concern themselves with it anymore. That's what spectator sports is all about.

This is kind of off point, but I've wondered about it: Doesn't the concept of DMU argue for wealth redistribution, assuming that utility, or happiness, is the ultimate objective? In other words, wouldn't the total amount of happiness in the world be greater if I gave more to the panhandlers every morning?

Or, is this reasoning fallacious because it is a partial analysis; redistribution destroys incentives, resulting in a significantly smaller pie, resulting in less for all, etc.

What we can say with certainty, using the concept diminishing marginal utility, is that the first dollar we give to Donald Trump will provide more pleasure than the fifth dollar.

With certainty? No, all we can really say is that usually, for many people, it seems to be the case that the fifth dollar has less utility than the first. To determine that this was true in an absolute sense would require showing it in neurology, I'd think.

Scott-
while you're right in an absolute sense, I think it's a reasonable pracitical assumption (see "the income effect.") When a dollar represents your meal for the night, it would almost certainly mean more than if a dollar just means a slightly higher number in your bank account. You can dispute this abstractly, but it certainly seems practically applicable.

Applying the concept of DMU you’d conclude that one dollar to starving person adds greater utility than does the same dollar given to Donald Trump.

Perhaps, but not with certainty. You are now making interpersonal comparisons, whereas your previous examples dealt with one person. What we can say with certainty, using the concept diminishing marginal utility, is that the first dollar we give to Donald Trump will provide more pleasure than the fifth dollar. It is a horse of a different color to compare utilities across different people.

Kevin,
I think you raise an interesting point- why do we even care about "my team." That seems to me a vestige of statism and other similar impulses. Make no mistake I do have a "team" (Broncos and 76ers), but I wish I could just enjoy a good game without caring which group of players who wear the same uniform win. It actually does seem very similar to statism and nationalism when looked at this way.

Nice post. The "heart is in the game" rationale strikes false to me, as well. That may have been true back in the day when college football and basketball were genuinely amateur athletics--when college athletics consisted mainly of people who'd already decided to go to a particular college, anyway, and then went out for a team. That's the way it still is in high school football. But now college athletics (the big money-generating sports, anyway) is governed by the same farm system as the pros: the kids who play college football are with a given team because the athletic department there offered the highest bid (plus wealthy alums probably slipped some added incentives under the table, as well). If some other university had offered a nickle more, they wouldn't be there.

That's why I have to roll my eyes at the people who enthusiastically refer to the local college team as "our team," and the students who talk about "school spirit."

...The fact that he has the money he has is evidence that he would work harder than someone who doesn’t have anything and is starving (likely do to with having traded his food stamps for crack).

The question is not whether Donald Trump works harder than a poor person. The question is whether who would be willing to work harder for a given amount of money. If you offered Trump $1000 to pick tomatoes all day, he'd probably laugh at you. But most poor people, even the lazy ones, would jump at the chance, because $1000 is worth so much more to them.

Matt,
An I would argue (not being an ecomimist) the fact that he has the money he has is evidence that he would work harder than someone who doesn't have anything and is starving (likely do to with having traded his food stamps for crack). Of course this only works for two people in the US, I am sure there are people in Africa or Asia who work there butts off for barely enough to feed themselves.

A great example of a player who will go to the wall while still never having to worry about money are the hockey enforcers. whats thier motivation? masochism? they get injured every time by getting bare knuckle punched in the face, and if they lose, its off to the minors.
they obviously 'love the game' as they're the lowest paid players by far. they instinctively know they must bust another guys face every night to stay in it. imagine if every day at work you had to fight another guy and pound him senseless or you didn't get paid anymore. wow!!! you would really have to love your job.:neutral:

Scott- I'd refer you to Descaretes meditiation 3 for a "proof" that the world exists (yeah right.) I doubt very highly that you'd have to demonstrate DMU via neurology (I realize you weren't neccesarily advocating that), because we're so far away from even being close to "demonstrating" something serious and insightful in that field. It's a practical consideration, just like the concept of "incentives" is.

I should also mention that being right that someone can't prove something "in the absolute sense" is really quite meaningless, as you seem to grasp with your mention of "proving" the existence of the outside world (something that's actually probably impossible.) You may as well be right "in the absolute sense" that we can't no for sure that the Holocaust happened or some other such nonsense.

Or, is this reasoning fallacious because it is a partial analysis; redistribution destroys incentives, resulting in a significantly smaller pie, resulting in less for all, etc.

Correct. See my comment in the "Live 8...Ignorance" thread on the undesirability of a system of allocation which maximizes short-term utility. But incentives are just part of the problem. The other part is the effect on savings. Almost by definition, recipients of redistributed wealth are not savers. And when you take money from people who have a positive savings rate and give it to people with a savings rate of zero or less, that's bound to reduce savings and slow growth.

Brandon you're clearly right to an extent, but the question is one of extent. Can you save nothing and still see long run economics growth? Maybe, but obviously the growth is aided by saving (actually investment which is a correlary, but not the same thing.) You do seem to be mistaking saving for investment a bit, which is somewhat dubious.

You didn't respond to any of my arguments though, so I'd prefer to wait until you do.

This is kind of off point, but I’ve wondered about it: Doesn’t the concept of DMU argue for wealth redistribution, assuming that utility, or happiness, is the ultimate objective? In other words, wouldn’t the total amount of happiness in the world be greater if I gave more to the panhandlers every morning?
yes, it has been used to argue this. A fellow named Owen actually rejected interpersonal comparisons of utility and said that we should just assume that dollaw utility is randomly distributed among the population. That was his argument for wealth equality.

Or, is this reasoning fallacious because it is a partial analysis; redistribution destroys incentives, resulting in a significantly smaller pie, resulting in less for all, etc.
I dunno- if you take the logic seriously it'd increase incentives by redirecting money in more efficient ways (one dollar becomes a much larger incentive to someone.)

Correct. See my comment in the “Live 8…Ignorance” thread on the undesirability of a system of allocation which maximizes short-term utility. But incentives are just part of the problem. The other part is the effect on savings. Almost by definition, recipients of redistributed wealth are not savers. And when you take money from people who have a positive savings rate and give it to people with a savings rate of zero or less, that’s bound to reduce savings and slow growth.

I don't know where you get "slow growth" from. There are plenty of reasons to prefer increased savings, but effects on growth isn't a very good one. Increased consumer spending tends to fuel growth.

I thought it was the general consensus that world growth has been heavily fueled by the US spending and lack of saving. This is the position of The Economist, as far as I can tell. Krugman may also be disregarding a worthwhile Keynesian idea- the liquidity trap. If spending starts to increase right now and the Fed cuts interests rates to turn it into investment then two things happen:
a. it can't cut rates very far, because rates can't go below zero
b. the incentive to loan money decreases (as there's less profit incentive.)

Mortgage Banks for instance would likely close their doors, or at least turn mainly to subprime markets. Investment isn't related to interest- it's related to rational expectation of the future. If the economy starts to slump, and Fed cuts interest rates, that may have no effect on investment. In fact, combining that with a narrowing profit incentive may simply convince people that they're in the wrong business.

You don't need to tell me that. My point was that this isn't just something made up by the free-market camp. I don't think any serious economist--not even Keynes--has disputed the idea that savings are the driving force behind long-run growth. What Keynesians say is that under certain circumstances the government may be able to make things run more smoothly by "stimulating" the economy in order to ensure that savings are channeled into productive investments.

The necessity of savings for growth is really quite obvious if you think about it. There are only two ways to increase real per-capita GDP. The first is for people to work more hours on average. Aside from being unpleasant, this can only take you so far. The other alternative is to increase labor productivity.

To increase labor productivity, you have to give laborers better tools to work with. It takes resources to produce those tools, so in order to increase labor productivity, an economy must shift resources away from producing consumer goods and towards producing capital goods. That's where savings come in. If an economy has a net savings rate of zero--i.e., it devotes all resources to producing consumer goods and replacing worn-out capital goods--there can be no growth.